Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 1 Chapter 13 Vision Based Guidance

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 2 Gimbal and Camera Reference Frames

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 3 Gimbal Reference Frames

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 4 Camera Reference Frame

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 5 Pinhole Camera Model Describes mathematical relationship between coordinates of 3-D point and its projection onto 2-D image plane Assumes point aperture, no lenses Good 1 st order approximation

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 6 Pinhole Camera Model image plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 7 Camera Model image plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 8 Camera Model image plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 9 Camera Model image plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 10 Gimbal Pointing Two scenarios –Point gimbal at given world coordinate “Point to this GPS location” –Point gimbal so that optical axis aligns with certain point in image plane “Point at this object” Gimbal dynamics –Assume rate control inputs

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 11 Scenario 1: Point Gimbal at World Coordinate

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 12 Scenario 2: Point Gimbal at Object in Image

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 13 Gimbal Pointing Angles

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 14 Gimbal Pointing Angles

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 15 Geolocation

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 16 Range to Target – Flat Earth Model

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 17 Geolocation Errors

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 18 Geolocation Using EKF

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 19 Geolocation Using EKF

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 20 GPS smoother geo-location attitude estimation vision processing gimbal Geolocation Architecture

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 21 Target Motion in Image Plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 22 Pixel LPF and Differentiation

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 23 Digital Approximation

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 24 Apparent Motion

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 25 Apparent Motion, cont.

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 26 Apparent Motion, cont.

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 27 Total Motion in Image Plane

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 28 Time to Collision

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 29 Time to Collision - Looming

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 30 Time to Collision – Flat Earth

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 31 Precision Landing

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 32 Proportional Navigation (PN)

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 33 Acceleration Command

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 34 Polar Converting Logic

Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 13: Slide 35 Polar Converting Logic, cont.